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    "# Regularization\n",
    "\n",
    "## Introductory Theory\n",
    "<p>Regularization is a technique for reducing the complexity of a model in supervised learning. The processing of performing regularization can be viewed with multiple interpretations:<br><br>\n",
    "\n",
    "<b><u>Complexity Penalty</u></b><br><br>\n",
    "\n",
    "In the ERM framework, regularization can be viewed as the penalty or cost for adding extra complexity to a model. Often, the complexity is a function of the weights learned for each feature. For now, we'll consider the class of linear models: $f(X) = W\\cdot X+t$. Remember in ERM we seek a function $f^{opt}$ such that:<br><br>\n",
    "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)$</center><br>\n",
    "\n",
    "where $\\mathbb{L}(f(x),y)$ is some arbitrary loss-function. The complexity of linear functions $f$ is set by the $L^p$-norm of the vector $W$, which is defined as $\\|W\\|_p =(|W_1|^p+|W_2|^p \\dots |W_m|^p)^{\\frac{1}{p}}$. The two norms we'll deal with the most in this class are $\\|W\\|_1$ and $\\|W\\|_2$. We want to add a term to the loss function that penalizes it as the norm of $W$ increases. We do this by adding a constraint to the above function:<br><br>\n",
    "\n",
    "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)$</center>\n",
    "<center>subject to $R(W)\\leq t$</center><br><br>\n",
    "\n",
    "where $R(W)$ can be any $L^p$-norm (mostly we'll choose $\\|W\\|_1$ or $\\|W\\|_2$). Using the method of Lagrange multipliers, we can set this up as:<br><br>\n",
    "\n",
    "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda (R(W)-t)=\\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda R(W)$</center><br><br>\n",
    "The parameter $\\lambda$ is the Lagrange multiplier here, and in most cases we choose it using some form of cross-validation or model selection. We can think of it as a lever that controls the amount of penalty we enforce as $R(W)$ increases. The most commonly used forms of regularization are:<br><br>\n",
    "\n",
    "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda \\sum\\limits_{j=1}^m |W_j|$</center><br><br>\n",
    "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda \\sum\\limits_{j=1}^m W_j^2$</center><br><br>\n",
    "\n",
    "The first one above is commonly called \"$L1$\" regularization or the \"lasso.\" The second is usually called \"$L2$\" or \"ridge.\" Both can be thought of as penalties that force the optimal solution into a bounded region, where the bound is defined by some sort of $L^p$ circle with radius $t$. <br><br>\n",
    "\n",
    "<b><u>Bayesian Formulation</u></b><br><br>\n",
    "\n",
    "Regularization also has a very nice Bayesian interpretation, which we will develop here. Regularization can be thought of as a Maxium a Posteriori estimation problem, which is an extension of Maximum Likelihood estimation. If you recall, we used the MLE method to find optimal parameters for Logistic Regression. This was defined as:<br><br>\n",
    "<center>$\\hat{\\beta}_{MLE} =\\underset{\\beta} {\\mathrm{argmin}} \\:L(\\beta|X,Y)=\\underset{\\beta} {\\mathrm{argmin}} \\:\\prod\\limits_{i=1}^nP(x_i,y_i|\\beta)=\\underset{\\beta} {\\mathrm{argmin}} \\:\\prod\\limits_{i=1}^np_i^{y_i}(1-p_i)^{1-y_i}$</center><br><br>\n",
    "\n",
    "In MAP estimation, we assert a prior belief onto the value of $\\beta$, so instead of finding $\\beta$ that optimizes the likelihood, we find one that optimizes the posterior distribution, which is defined as:<br><br>\n",
    "\n",
    "<center>$P(\\beta|X,Y) = \\frac{P(X,Y|\\beta)*P(\\beta)}{P(X,Y)}$</center><br><br>\n",
    "Usually with MAP, the denominator above doesn't factor into the optimization, so we only consider:<br><br>\n",
    "<center>$P(\\beta|X,Y) \\propto P(X,Y|\\beta)*P(\\beta)=Likelihood*Prior$</center><br><br>\n",
    "For logistic regression, we have already defined the likelihood. Now we can define a prior on $\\beta$. For reasons of mostly mathematical convenience, we can assume that $\\beta$ comes from one of two priors:<br><br>\n",
    "<center>$P(\\beta_j) = N(0,\\tau_j)=\\frac{1}{\\sqrt{2\\pi \\tau_j}}exp(\\frac{-\\beta_j^2}{2\\tau_j}),\\: \\:j=1,2,\\dots d$</center><br>\n",
    "or\n",
    "<center>$P(\\beta_j) = \\frac{\\lambda_j}{2}exp(-\\lambda_j|\\beta_j|), \\: \\:j=1,2,\\dots d$</center><br><br>\n",
    "\n",
    "The first above is the normal distribution, and the second is the Laplace distribution. Again, there might be no reason to assume one prior is better (or more accurate) than the other. We normally choose based on properties of the MAP, given a specific prior. Also, we defined the above priors as functions of individual parameters $\\beta_j$. We usually assume that the prior on each $\\beta_j$ is independent, so that $P(\\beta)=\\prod\\limits_{i=1}^d P(\\beta_j)$. We can now define a new optimization task, based on the MAP formulation:<br><br>\n",
    "\n",
    "<center>$\\hat{\\beta}_{MAP} =\\underset{\\beta} {\\mathrm{argmax}} \\:L(\\beta|X,Y)\\:P(\\beta)$</center><br><br>\n",
    "Using the above priors, we can define two different MAP estimators.<br><br>\n",
    "\n",
    "\n",
    "<center>$\\hat{\\beta}_{MAP}=\\underset{\\beta} {\\mathrm{argmax}} \\prod\\limits_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i} \\: \\prod\\limits_{j=1}^d \\frac{1}{\\sqrt{2\\pi \\tau_j}} exp(\\frac{-\\beta_j^2}{2\\tau_j})$</center><br>\n",
    "or\n",
    "<center>$\\hat{\\beta}_{MAP}=\\underset{\\beta} {\\mathrm{argmax}} \\prod\\limits_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i} \\: \\prod\\limits_{j=1}^d \\frac{\\lambda_j}{2}exp(-\\lambda_j|\\beta_j|)$</center><br><br>\n",
    "\n",
    "We don't try to optimize these functions as is. Instead we take the log, and in doing so, we end up with equivalent formulation of $L1$ and $L2$ regularization defined above.\n",
    "\n",
    "</p>"
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    "## Examples"
   ]
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    "<p>As a starting point, we can visualize how regularization constrains our search space for possible optimum values of $\\beta$. We'll generate a high variance data set that represents a bournoulli process where $P(Y|X)$ is governed by the inverse logit. We'll then plot the following:\n",
    "<ul>\n",
    "    <li>Contour plot of the log-likelihood loss as a function of $\\beta$</li>\n",
    "    <li>Constraint boundaries of the following constraint $|\\beta|_p<t$</li>\n",
    "    <li>The path of $\\hat{\\beta}_{MAP}$ as we vary regularization strength</li>\n",
    "</ul>\n",
    "</p>"
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    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "#sys.path.append(\"C:/Users/kevin/Documents/GitHub/DS_course/ipython\")\n",
    "\n",
    "import course_utils as bd\n",
    "from sklearn import linear_model\n",
    "from matplotlib.colors import BoundaryNorm\n",
    "from matplotlib.ticker import MaxNLocator\n",
    "import imp\n",
    "imp.reload(bd)\n",
    "\n",
    "\n",
    "def RegDemo(n, alpha, beta, regtype):\n",
    "    #Generate a bivariate X and a bournoulli Y\n",
    "    data = bd.gen_logistic_dataframe(n, alpha, beta)\n",
    "\n",
    "    #Create a grid of possible combinations of beta\n",
    "    dy = 0.1; dx = 0.1 ; b_min = 0; b_max = 2\n",
    "    b1, b2 = np.mgrid[b_min:b_max:dx, b_min:b_max:dy]\n",
    "\n",
    "    #Get z\n",
    "    z = np.array([[ bd.LogLoss(data, [b1[i,j], b2[i,j]], 0) for j in range(b1.shape[0])] for i in range(b2.shape[0])]) \n",
    "    z = z[:-1, :-1]\n",
    "\n",
    "    #Some settings\n",
    "    levels = MaxNLocator(nbins=15).tick_values(z.min(), z.max())\n",
    "    cmap = plt.get_cmap('PiYG')\n",
    "    norm = BoundaryNorm(levels, ncolors=cmap.N, clip=True)\n",
    "\n",
    "    #Plot Contour\n",
    "    fig = plt.figure()\n",
    "    ax = plt.subplot(111)\n",
    "\n",
    "    plt.contourf(b1[:-1, :-1] + dx / 2., b2[:-1, :-1] + dy / 2., z, levels=levels, cmap=cmap)\n",
    "    plt.colorbar()\n",
    "\n",
    "    #Plot an Lp Constraint, i.e., the Lp norm < k\n",
    "    cs = [0.5, 1, 1.5, 2, 2.5, 3]\n",
    "    x_c = np.arange(b_min, b_max, 0.01)\n",
    "    for c in cs:\n",
    "        if (regtype==2):\n",
    "            y_c = np.sqrt(c - x_c**2)\n",
    "            plt.plot(x_c[~np.isnan(y_c)], y_c[~np.isnan(y_c)], label='L2 norm<{}'.format(c))\n",
    "        else:\n",
    "            y_c = c - x_c\n",
    "            plt.plot(x_c[(y_c>0)], y_c[(y_c>0)], label='L1 norm<{}'.format(c))\n",
    "\n",
    "\n",
    "    #Now get optimums for various regularization strengths\n",
    "    b1_opt = []\n",
    "    b2_opt = []\n",
    "    for i in range(-10, 10):\n",
    "        LR = linear_model.LogisticRegression(C=10**i)\n",
    "        LR.fit(data.drop('Y', 1), data['Y'])\n",
    "    \n",
    "    #Now fit the data for various regularization strengths\n",
    "    b1_opt = []\n",
    "    b2_opt = []\n",
    "    for i in range(-60, 60):\n",
    "        LR = linear_model.LogisticRegression(C=10**i, penalty='l{}'.format(regtype))\n",
    "        LR.fit(data.drop('Y', 1), data['Y'])\n",
    "        b1_c, b2_c = LR.coef_[0]    \n",
    "        b1_opt.append(b1_c)\n",
    "        b2_opt.append(b2_c)\n",
    "\n",
    "    plt.plot(b1_opt, b2_opt, 'k+-')\n",
    "    \n",
    "    plt.xlim([b_min+dx, b_max-2*dx])\n",
    "    plt.ylim([b_min+dy, b_max-2*dy])\n",
    "\n",
    "    box = ax.get_position()\n",
    "    ax.set_position([box.x0, box.y0 + box.height*0.0 , box.width, box.height * 1])\n",
    "\n",
    "    # Put a legend below current axis\n",
    "    ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), fancybox=True, shadow=True, ncol=3, prop={'size':10})\n",
    "\n",
    "    plt.show()\n"
   ]
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    "<p>The next two plots show all of the above with different sized datasets. The first is relatively small, with 50 examples, and the 2nd has 50k examples. We know the true value of the data generating distribution is $\\beta=[1, 1]$. The dark green elipsoid shows where the log-loss is at a minimum. Its center is the optimum point of the data. With more data, we can see that this center gets closer to $[1, 1]$.<br><br>\n",
    "The circular constraint boundaries basically say that the coordinates of $\\hat{\\beta}_{MAP}$ have to be within that boundary. The MAP estimator will found the lowest value of the log-loss (i.e., darker color) within the circle. <br><br>\n",
    "\n",
    "What we can learn here is that with a very loose regularization weight (bigger circle), we are more likely to choose $\\hat{\\beta}_{MAP}$ that fits the data well, but is far from the truth (which we know because we created the data generating distribution). With the right regulariztion strength (such as the red circle in the above plot), we can see that our MAP estimate is actually closer to the truth. The problem is less severe with more data, because the dark green elipsoid shifts closer to the true optimum point. <br><br>\n",
    "\n",
    "Note that with $L1$ regularization, we can do the same analysis, though the constraint boundaries would look different. Instead of circles they would be straight lines.\n",
    "\n",
    "</p>"
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X1kNTGdqH69F234Y6uor42v1Q2jBnIjAe473H6oKVZFW6qfrPq2h/NeEFDJya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\nlvC3sLCwGIFYwt/CwsJiBPL/AO1FojoBJTg2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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l7Ijdwh9F7qRbO8CL1p8wqmWmSmRvZ/SkF+DLC/LSuS00dJZR019Moc/FkfU9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\niYgoXvioJxGRhrj8iYg0xOVPRKShf5Uolh/0pUyIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "RegDemo(50, 0, [1, 1], 2)\n",
    "RegDemo(50000, 0, [1, 1], 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The above examples were a bit theoretical, and are mainly presented for explaining the underlying optimization process (and to reinforce the idea of the bias-variance tradeoff going on).<br><br>\n",
    "Below we'll look at an actual dataset. First we'll read it in and rescale it. Rescaling is very important because the norm of $\\beta$ is going to be a function of the scale of each feature. Since we apply the same regularization factor to each feature, rescaling ensures that it has the same effect per feature. \n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import scale\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import linear_model\n",
    "imp.reload(bd)\n",
    "\n",
    "f='../data/ads_dataset_cut.txt'\n",
    "\n",
    "#Lets prep the data\n",
    "train_split = 0.75\n",
    "tdat = pd.read_csv(f,header=0,sep='\\t')\n",
    "\n",
    "'''\n",
    "For regularization, it is advised to normalize the data first. We'll normalize and then split, and if its not obvious\n",
    "we shouldn't normalize the outcome.\n",
    "\n",
    "Note too that the sklearn scale function returns an array, which we have to throw back into a data frame.\n",
    "'''\n",
    "\n",
    "lab = 'y_buy'\n",
    "Y = tdat[lab]\n",
    "X = tdat.drop(lab, 1)\n",
    "X_scale = pd.DataFrame(scale(X, axis=0, with_mean=True, with_std=True, copy=True), columns = X.columns.values)\n",
    "\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X_scale, Y, test_size=0.3, random_state=42)\n",
    "\n",
    "#The above returns numpy arrays. I'd prefer to store them as data frames.\n",
    "X_train = pd.DataFrame(X_train, columns = X.columns.values)   \n",
    "X_test = pd.DataFrame(X_test, columns = X.columns.values)   \n",
    "Y_train = pd.Series(Y_train)    \n",
    "Y_test = pd.Series(Y_test)        \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Next, we'll look at how a feature's weight evolves as we change the regularization weight.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "L2 = {}\n",
    "L1 = {}\n",
    "\n",
    "for i in np.arange(-5, 5, 0.5):\n",
    "    LR2 = linear_model.LogisticRegression(C=10**i, penalty = 'l2')\n",
    "    LR2.fit(X_train, Y_train)\n",
    "    L2[i] = LR2.coef_[0]\n",
    "    LR1 = linear_model.LogisticRegression(C=10**i, penalty = 'l1')\n",
    "    LR1.fit(X_train, Y_train)\n",
    "    L1[i] = LR1.coef_[0]\n",
    "\n",
    "\n",
    "feats = X.columns.values\n",
    "Rpath2 = pd.DataFrame(L2, index=feats).transpose()\n",
    "Rpath1 = pd.DataFrame(L1, index=feats).transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> This plot shows how the weights progress with $L2$ regularization. We can see a generally smooth progression that converges to a point as the regularization strength decreases.\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x400 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LkhwLIRwqPjmd8N2xhEWcZPepeJxMigeb1aVfUAPub1IbJ1ldQgghRCmS5FgI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\n1QDExMSwfft22rRpw5IlS2jfvj0+Pj6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uLuSuCybz8ZmVzD+tBN0TkAnLZvXG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PL293n9jwtYUVJF/d6GDjm+iIh82m233cZjjz3GmDFj2LhxY7vU+eyzz/L73/+ekSNHcvrpp1NR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\nJCIi3ZSSY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TkqPS45FhERERFpTY/rViEiIiIi0holxyIiIiIiPiXHIiIiIiI+JcciIiIi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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "for f in feats:\n",
    "    plt.plot(Rpath2.index.values, Rpath2[[f]], label=f)\n",
    "\n",
    "plt.xlim([-3, 2])\n",
    "plt.ylim([-1, 1])\n",
    "box = ax.get_position()\n",
    "ax.set_position([box.x0, box.y0, box.width*1.5, box.height * 1.5])\n",
    "\n",
    "    # Put a legend below current axis\n",
    "ax.legend(loc='upper center', bbox_to_anchor=(1.15, 1), fancybox=True, shadow=True, ncol=1, prop={'size':10})\n",
    "\n",
    "plt.title('L2 Regularization Paths for Feature Weights.')\n",
    "plt.xlabel('Regularization weight C (higher C is less regularization)')\n",
    "plt.ylabel('Feature Weight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> Next we'll do the same for $L1$.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x400 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kJDBgwADi4+Mrve9PPvkER0fHaxbPKC4uLo6zZ8/Sv3//Sj9/cXfyed5tkgAL\nUYMcOJfGB78eYUAbH/q39rn5AbVYXoGxRLJamLz+uS2fzNyCUklt2W2zcgvIN1bfRYWUujOJ6p24\nIjVs7SYhbur555+/aZu4uDhiYmIqlADn5+djbV1708Da+8yFqGEKSx9cHWyYWcNLH/ILjBy+kEFK\nVq4pGc3NJ8M84nq9ZLWwXeG23Hxjuc5lbaVwsrPG2c4aJzsDTnbWuNhbU7+OvXm7adufbUpuc7Q1\nYKVM42xKqaJkUxVtM43CKWX+e1nbAcyPrcpog/ozibUqOocqGoUs/tiq+LHVZZiymqkuK6xWkzAB\nMLxTvnbn33qLnAMHK/Xcdi1bUP/112/aLj8/n+HDh7Nz506CgoJYvHgxgYGBRauuxcTEMHHiRNav\nX09AQABbtmzBy8sLo9FI8+bNiY6OxsvL65p+p0+fjrOzMxMnTqR79+6Eh4ezYcMGUlJSWLhwIeHh\n4bz55ptcvXqVzZs3849//IMBAwYwduxY4uPjycvLY/r06QwaNIjIyEi+/fZbMjIyKCgowMfHhxEj\nRvDQQw8BMHLkSAYMGEBoaCgjRowgMzMTgAULFtCpU6dKva6WJgmwEDXERxuOse9sGp9EhODuZGvp\ncCpVgVGz72wq0ccuEX38EjtOXCYzt6DMtkqBk+2fyaqznTVOttY0rOtYlJgWJqplJrC2JZNdO2sr\nSRRFhVSX90s1CbPaOHToEAsXLqRz586MHj2ajz76qMx2VlZWREREsGTJEiZMmMC6deto27Ztmclv\nWfLz89m+fTtr1qxhxowZrFu3jpkzZxITE8OCBQsAeP311+nRoweLFi0iJSWFsLAwHnzwQQB27tzJ\nnj17cHd357vvvuObb77hoYceIjc3l19//ZWPP/4YrTVr167F3t6eI0eOMGzYMGJiYirnQlURkgAL\nUQPsO5vK/PVHGBTsS99W9S0dzm0zGjUHzqcRfewSW49fYtuJy6Rn5wNwj5cTj7RrQFgTd+q52Bcl\nq4VJrYONASsr+c0uRG1UnpHaO8XPz4/OnTsDEBERwbx5867bdvTo0QwaNIgJEyawaNEiRo0aVe7z\nPProowCEhIRcd1W3X375hVWrVjFnzhwAsrOzSUxMBKBXr164u7sD0K9fP8aPH09OTg4//fQT3bp1\nw8HBgdTUVF5++WXi4uIwGAwcPny43PFVF5IAC1HN5eYbmbh8D26Otkx/OMjS4dwSrTWHL2QQfewi\n0eaENyUrD4DGHo481NqHjk096HCPB951ZDlnIUTVU3rkXymFtbU1RqOp3Co7O7ton5+fH97e3qxf\nv57t27ezZMmScp/Hzs50c7MKGPSeAAAgAElEQVTBYCA/P7/MNlprVqxYQUBAQInt27Ztw8nJqeix\nvb093bt35+eff2bZsmU8+eSTALz//vt4e3uze/dujEYj9vY1799dSYCFqOYWbDjKgXNpfDoihLrV\npPRBa82x5Eyij19iq3mU91JmLgAN3Bx4sKU3He/xoGNTD3zdHCwcrRBC3FxiYiLR0dF07NiRpUuX\n0qVLF9LT04mNjaVfv36sWLGiRPsxY8YQERHBiBEjMBgMt3VuFxcX0tPTix736dOH+fPnM3/+fJRS\n7Nq1i3bt2pV57NChQ/nss8+IiYkhMjISgNTUVBo2bIiVlRVffPEFBQVll5xVZ5IAC1GNxZ9J5aMN\nRxncrgG9g6pu6YPWmpOXsog+fqmorCEpPQeA+nXs6dbcqyjh9XN3tHC0QghRcQEBAXz44YeMHj2a\nwMBAXnjhBcLCwnj22WeZOnUq3bt3L9F+4MCBjBo1qkLlD9fzwAMPMHv2bIKDg/nHP/7B1KlTmTBh\nAm3atMFoNNKkSRNWr15d5rG9e/dmxIgRDBo0CFtb0yDKiy++yGOPPcbixYvp27dviVHjmkJVl7tV\nyys0NFTXtEJtIcqSm29k4ILNXM7M5ZdXuuHmWLVGf09fySq6aW3rsUucTTV9/efpbEfHph5FCa+/\nh2O1uWlICGEZSqlYrXVoWftiY2N1SEjI3Q7ptsXExPDKK6/w+++/WzqUGi02NpYZM2YsBGauWrUq\nsXC7jAALUU3NX3+Eg+fTWfhMaJVIfs+nZhN9/GJR0nvq8lUA3J1s6XCPOy+YE96mXs6S8AoharXZ\ns2fz8ccfV6j2V1QuSYCFqIb2nE7ho43HeOy+hvRs6W2RGJLSs9l6/HJRScOJi6b5Il0dbAhv4s7o\nzk3o2NSD5vVcZFYGIYQoZvLkyUyePLnEtlmzZrF8+fIS24YMGcKUKVPuZmi1hiTAQlQzOfkFTFy+\nG09nW958OPCunfdyZi5bzTW80ccvcTQpAwAXO2vCmrgzPLwRHe7xoKVPHQyS8AohRIVMmTJFkt27\nSBJgIaqZD9Yd4fCFDD4f1R5XB5s7dp7UrDy2nvjzprWD5013GDvaGmjv787jIQ3peI8HQb51sDZY\n3bE4StNGTWb0WdI2nELnFBRbw7fUer6q6D9FK6Vds+9G7Ys9LLNt8Q6L71Z/9gGg7Aw4hdbHKaQe\nyub27vQWQghROSQBFqIaiTuVwie/HeOJ0IY8EFCv0vtPzcrj09+PsfFQMvvPpaE12NtYEdrYndf6\n+NLhHg/aNHTF5i4mvMXlXcjkyooj5CamY3evGza+TqAx/SlUeGOvLr6p+INS7Uq1RVe0vTY9LCsG\nIP9SNinfHyVt7UmcO/ni1MEHg9Od++AihBDi5iQBFqKayM4zlT5417HnjQGVW/qgtea7XWd4a80B\nLmfmEtbEnQk9m9OxqQdt/Vyxs7bsyKXON5K+8RRpG05hZWeg7tAAHIO9qsXNdFprck+kkr7pDGlr\nT5K+8RSOod64dG2ItXvNm1xeCCGqA0mAhagm3l93mKNJGXwxOow69pU3gnj4QjpvfB/P9hOXCfZz\nI3JUGK0auFZa/7crJzGNKyuOkH8hC4dgL9wG3IPB2fKzXpSXUgq7e9ywu8eNvAuZpG86Q+b282Ru\nPYdDa09cujXEtqGLpcMUQohaRRJgIaqBnYlX+M+m4wwL8+P+5l6V0mdWbj7zfj3KZ78fx8nOmrcG\nt+bJ9n5VZsYGY04Bab8kkLHlLIY6dniMDMKhhbulw7otNt5OuA9pjmvvxqRvOUvm1nNc3XMRu3tc\ncb6/IfbN61aLUW0hROXq378/S5cuxc3N7bptIiMj6d27N76+vnc0lunTp+Ps7MzEiRPv6HksTRJg\nIaq4wtIHH1cHXu/f8rb701rzy/4LzPzffs6kXOXxkIb8o18LPJztKiHaypF9+ApXvj1CQWoOTh18\ncO3rj5VdzfnnyuBqh1u/JtR5wI/M7efJ2HyGS5/vw9rbEZduDXFs64WytkydtRDi7luzZs1N20RG\nRtKqVasKJcD5+flYW9ecfzsrk1wVIaq4//vlEMeTM/nq2XBcbrP04dTlLKav2sevB5MI8Hbhm+c6\nEtak6oyqFmTmkbr6OFm7krD2csDruTbY+VedcozKZmVvjUu3hjh38iVrdzLpm05zZflh0n5OwLlL\nA5zC6mNlL/9MC1Fev39zmIunMiq1T08/Z7o+0fyGbTIzM3niiSc4ffo0BQUFvPbaa6xevbpoXt+N\nGzcyZ86c6y5H7O/vT0xMDBkZGfTr148uXbqwZcsWGjRowMqVK/nhhx+IiYlh+PDhODg4EB0dzf79\n+3n11VfJyMjA09OTyMhIfHx86N69O8HBwWzevJmHH36YRYsWceLECaysrMjMzKRFixYcP36cyMhI\nPv30U3Jzc7n33nv58ssvcXSsPUvRyxCDEFVY7MnLfLb5BE+FN6JLM89b7icnv4APNxyl1/u/EX38\nElP6t2T1uC5VJvnVWpMVl8SF92LJ2p2MSw8/vMffV6OT3+KUtRVOId54T7gPz1FBWHs5kLrmBOfe\n3k7KjycoSMuxdIhCiBv46aef8PX1Zffu3cTHx/PII4+wbds2MjNNCwQtW7aMJ598slx9HTlyhJde\neol9+/bh5ubGihUrePzxxwkNDWXJkiXExcVhbW3N2LFjiYqKIjY2ltGjR5eYQzg3N5eYmBimTZtG\ncHAwv/32GwCrV6+mT58+2NjY8Oijj7Jjxw52795Ny5YtWbhwYeVfmCpMhhaEqKKu5hYwcfkefG+z\n9OGPoxeZujKe48mZ9GtVn6kDAvF1c6jESG9PfkoOKd8fJfvgZWz8XPB6rBk29Z0sHZZFKKWwD3DH\nPsCd3NPppG86Tcam02RsPoNjcD1cujXAxrt2XhshyuNmI7V3SuvWrfnb3/7GpEmTGDBgAF27dqVv\n377873//4/HHH+eHH37g3XffLVdfTZo0ITg4GICQkBASEhKuaXPo0CHi4+Pp1asXAAUFBfj4+BTt\nHzp0aIm/L1u2jAceeICvv/6aF198EYD4+HjeeOMNUlJSyMjIoE+fPrf69KslSYCFqKLm/HKIExcz\nWTomHOdbqH9NSsvmXz8cYNXuszRyd+TzUe3vyNzBt0obNZnbzpH6UwIYNa4D7sG5ky+qityEZ2m2\nDV3weKol+Zeukr75DFkxF8iKvYB9C3dcujXAtomr3DAnRBXRvHlzdu7cyZo1a3jjjTfo2bMnTz75\nJAsWLMDd3Z3Q0FBcXMo324ud3Z/3YxgMBq5evXpNG601QUFBREdHl9mHk9OfH5QHDhzI66+/zuXL\nl4mNjaVHjx4AjBw5ku+//562bdsSGRnJxo0bK/CMqz9JgIWografuMyiP04wokNjOt1bsdKHAqPm\ny+gE/u+Xw+TkGxnXsxkvdm+KfRVahSwvKcu0oMXJNOyauVF3cDOZE/c6rD0cqDvoXuo82JjMrefI\n2HKW5E/3YuPngku3BjgEecqHBiEs7OzZs7i7uxMREYGbmxufffYZU6ZMYfTo0fznP/8pd/nDjbi4\nuJCeblqRMyAggOTkZKKjo+nYsSN5eXkcPnyYoKCga45zdnamffv2jB8/ngEDBmAwmH4XpKen4+Pj\nQ15eHkuWLKFBgwa3HWN1IgmwEFVMVm4+r0XtpmFdByb3a1GhY+NOpTDlu73sO5tG12aezBzUiiae\nVecrc51vJP2306StTzQtaDGkOY731ZORzHIwONlQp2cjXLo1IDM2iYzfT3N5yUEMHva4dGmAY4g3\nVrZV50OOELXJ3r17ee2117CyssLGxoaPP/4Yg8HAgAEDiIyM5Isvvrjtc4wcOZLnn3++6Ca4qKgo\nxo0bR2pqKvn5+UyYMKHMBBhMZRBDhgwpMcr7z3/+k/DwcLy8vAgPDy9KrmsLVWLJzxogNDRUx8TE\nWDoMIW7Z9FX7iNySwH//0oGOTT3KdUxqVh7v/HyQ/25PxMvZjjcfDuSh1j5VKrHMPZXOlRWHyTuf\nhUMbT9weborBpfosaFHVaKMme/8l0n87Te6pdKycrHHu6ItTR19ZalnUOEqpWK11aFn7YmNjdUhI\nyN0OSVQTsbGxzJgxYyEwc9WqVYmF22UEWIgqZOvxS0RuSWBkJ/9yJb9aa1bsPMPbaw5wJSuXUZ2a\n8EqvZrc9XVplMuYWkPbLSTL+OIPBxRaPpwNxCCxfYi+uT1kpHFp5Yh/kQW5CGumbTpO2LpH0307j\nGOKNS9cGWHtUnZsdhRCiKpEEWIgqIjMnn79H7aGxhyN/7xtw0/aHzqcz9ft4tidc5r5Gbix+Nowg\n36o1bVj2EfOCFleKLWgh89pWKqUUdk1csWviSl5SFumbTpO54zyZ287h0Mq81LKfLLUsRFUQHh5O\nTk7JaQ2//PJLWrdubaGIai/5TSREFfHOTwc5dSWLZX/tiKPt9X80M3PymffrERZuPoGzvTWzH23N\nE6FVZwljAGNWHimrj5O1MwlrT/OCFk2qVnJeE9nUc8T98ea49vYnY8sZMrae4+rei9g2ccXl/obY\nB8hSy0JY0rZt2ywdgjCTBFiIKmDLsYssjj7JqM7+112cQmvNz/suMPN/+zibms3QUD8m9WuBu1PV\nqaPVWnN170VSVh3DmJWPywN+1OnRCGUja+7cTYY6trj2bYJL8aWWI81LLXdtiGOwLLUshKjdJAEW\nwsIyzKUP/h6O/L1P2bM+JF7KYtqqeDYcSqZFfRfmDWtHqH/VWMWtUH6qeUGLA5exaeiM5+hW2Po6\nWzqsWs3KzhqXruallvdcJOO3U1yJOkzaLwk4d26AU7gstSyEqJ3kXz4hLOztNQc4k3KV5c91xKHU\nNFY5+QV8+ttxFmw4irWV4o2HWjKykz/WhqozeqeNmszt50n98YRpQYv+TXDu3ABlkK/aqwplsMKp\nXT0cg73IOZJC+qbTpP54grT1iTiF18e5cwOsXe1u3pEQQtQQkgALYUGbj1xkybZExnRpcs2I7uYj\nF3lzZTzHL2byUGsf3hjQEh/XqnVXf16yeUGLhDTs7nWj7uB7ZeaBKkwphX3zutg3r0vumQzTUsub\nz5Cx+SyObb1wau+Nrb+rLKwhhKjxqs4wkhC1THp2HpNW7OEeTycm9vlz1ocLadmM/e8uIhZuo0Br\nIke158Ph91Wp5FcXGEnbkMiFD3aSdz6Luo83w/PZVpL8ViO2DZzxGNaC+hPb49zBh6v7L5H86V7O\nz4khbd1J8i9nWzpEIcQNJCQksHTp0gofN3LkSKKioq67f+7cuWRlZRU97t+/PykpKbcU481ERkby\n8ssv35G+b0ZGgIWwkLfWHORc6lWWP98JexsD+QVGFkef5L21h8ktMDLhwWY8f3/VWsIYIPd0OldW\nHCHvXCYOrT1xGygLWlRn1u72uA1sSp2+/mTvu0Rm7AXSfk0kbV0idk1dcQzxxqGVp6wyJ0QVU5gA\nP/XUU5Xa79y5c4mIiMDR0RGANWvWVGr/VYUkwEJYwKbDyfx3eyLPdbuHkMZ12Zl4hTe+i2f/uTS6\nNfdi5sAg/KvQEsZgXtBi7UkyNp/BytkWjxEtcQjytHRYopJY2RpwbFcPx3b1yL+STdbOJDJjL3Dl\nm8OkrDyGQ2tPnEK9sW1cR6ZSE1XWhshPSTp5vFL7rNf4Hh4Y+debtvvqq6+YN28eubm5hIeH8/rr\nr/Pggw8SHR2Nu7s7999/P1OnTqV58+b07duXkJAQdu7cSVBQEIsXL8bR0ZHY2FheffVVMjIy8PT0\nJDIyEh8fH44ePcrzzz9PcnIyBoOB5cuXM3nyZA4cOEBwcDDPPPMM48aNY/LkyWzcuJGcnBxeeukl\nnnvuObTWjB07lrVr1+Ln54et7fUHLObNm8fZs2d54IEH8PT0ZMOGDfj7+xMTE0NGRgZ9+/alQ4cO\nbNmyhfbt2zNq1CimTZtGUlISS5YsISwsjMzMTMaOHUt8fDx5eXlMnz6dQYMGXfecp06donv37pw5\nc4aIiAimTZtGQkICAwYMID4+HoA5c+aQkZHBiBEjGDJkCDt37gTgyJEjDB06tOhxRUgCLMRdlmYu\nfWjq5cToLv7849u9fL0jEW8Xez4afh/9WtWvcglG9tErXPn2KAWXs3EKq49rvyZYOcg/HzWVdV17\n6vRshEsPP3IT0siMucDVPclkxVzA2sMexxBvHO/zxtpNbpwTAuDAgQMsW7aMP/74AxsbG1588UV+\n++03Jk2axAsvvEBYWBiBgYH07t2bhIQEDh06xMKFC+ncuTOjR4/mo48+Yvz48YwdO5aVK1fi5eXF\nsmXLmDJlCosWLWL48OFMnjyZwYMHk52djdFoZPbs2cyZM4fVq1cD8Omnn+Lq6sqOHTvIycmhc+fO\n9O7dm127dnHo0CH279/PhQsXCAwMZPTo0WU+j3HjxvHee++xYcMGPD2vHeA4evQoy5cvZ9GiRbRv\n356lS5eyefNmVq1axVtvvcX333/PrFmz6NGjB4sWLSIlJYWwsDAefPBBnJzKHtTZvn078fHxODo6\n0r59ex566KEyzw3QtGlTXF1diYuLIzg4mM8//5xRo0bd0msmv8GEuMtmrT7AhbRsXux+L/0+2Ezq\n1Tye7dyECb2a42xXtX4kjVl5pPxwgqzYC6YFLf7aGrt73CwdlrhLiq8yZxzYlKvxF8mKvUDaLydJ\nW3sSu3vdcArxxiHIA1XFSnVE7VSekdo74ddffyU2Npb27dsDcPXqVerVq8f06dNZvnw5n3zyCXFx\ncUXt/fz86Ny5MwARERHMmzePvn37Eh8fT69evQAoKCjAx8eH9PR0zpw5w+DBgwGwt7cvM4ZffvmF\nPXv2FNX3pqamcuTIETZt2sSwYcMwGAz4+vrSo0ePW36eTZo0KVq1LigoiJ49e6KUonXr1iQkJBTF\nsWrVKubMmQNAdnY2iYmJtGzZssw+e/XqhYeHBwCPPvoomzdv5pFHHrluDGPGjOHzzz/nvffeY9my\nZWzfvv2WnotFf9sqpfoCHwAG4DOt9exS+18FxgD5QDIwWmt98q4HKkQl2XAoiWUxp6jvas+CDUcJ\naVyXfz3SipY+dSwdWglaa67GXyRl5TGMWXm4dG9InZ6NJMmpxazsDDiFeOMU4k3+5WwyYy+QtfMC\nl78+hLIz4NjWC8cQb2wbuVS5bzCEuNO01jzzzDO8/fbbJbZnZWVx+vRpADIyMnBxMS1LXvpnRCmF\n1pqgoCCio6NL7EtPTy93DPPnz6dPnz4ltldmDa+d3Z/f+lhZWRU9trKyIj8/vyiOFStWEBAQUGYf\npZV1LaytrTEajUXbsrP/vCn3scceY8aMGfTo0YOQkJCi5LmiLDYLhFLKAHwI9AMCgWFKqcBSzXYB\noVrrNkAU8O7djVKIynMu5SovLzHVKWXn5vPuY21Y/lzHKpf8FqTlcOnLA1xechCDqx31XmqHa98m\nkvyKItbu9rj2akz919rj+ZfWOAR5kLUrieSPd3PhvVjSNp6iIDXH0mEKcdf07NmTqKgokpKSALh8\n+TInT55k0qRJDB8+nJkzZ/KXv/ylqH1iYmJRort06VK6dOlCQEAAycnJRdvz8vLYt28fLi4uNGzY\nkO+//x6AnJwcsrKycHFxKZEc9+nTh48//pi8vDwADh8+TGZmJt26dWPZsmUUFBRw7tw5NmzYcMPn\nUrrfiurTpw/z589Haw3Arl27bth+7dq1XL58matXr/L999/TuXNnvL29SUpK4tKlS+Tk5BSVeYBp\nBLxPnz688MILt1z+AJYdAQ4DjmqtjwMopb4GBgH7CxtorYu/SluBiLsaoRCVZPuJSzyzaAdX8wro\nHViPdx5rS90qtIRxoavxF7kcdQSdb8S1nz/OXRrKghbiupSVwr6pG/ZN3TAOasrVPRdNs0j8lEDa\nzwnYNatrKpEI9JDlsEWNFhgYyL/+9S969+6N0WjExsaG9957jx07dvDHH39gMBhYsWIFn3/+OQ88\n8AABAQF8+OGHjB49msDAQF544QVsbW2Jiopi3LhxpKamkp+fz4QJEwgKCuLLL7/kueee480338TG\nxobly5fTpk0bDAYDbdu2ZeTIkYwfP56EhATuu+8+tNZ4eXnx/fffM3jwYNavX09gYCCNGjWiY8eO\nN3wuf/3rX+nbty++vr43TZbLMnXqVCZMmECbNm0wGo00adKkRAJbWlhYGI899hinT58mIiKC0NBQ\nAN58803CwsJo0KABLVqUXCV1+PDhfPfdd/Tu3bvC8RVShRn63aaUehzoq7UeY348AgjXWpc5IZxS\nagFwXmv9rzL2/RX4K0CjRo1CTp6UKglRNeQXGPng1yPMX38UgKHtG/LOY20tHNW1dL6R1DUnyNhy\nFpuGzrg/2QIbT5nTV9ya/ItXydx5gazYJApSc1D21jgGe+EU4o1NQ2cpkRAVppSK1VqHlrUvNjZW\nh4SE3O2QblnpGQ5Exc2ZM4fU1FT++c9/3rRtbGwsM2bMWAjMXLVqVWLh9qp1x811KKUigFDg/rL2\na60/BT4FCA0NtUxGL0QpZ1KuMm7pLmITrwAwtse9vNqruYWjulb+patcWnqQvDMZOHf2xbVfE5S1\njNaJW2ft6YBrb3/qPNiYnGMpZMVeIDPmAplbz2FdzxGnEG8c76sn80cLISps8ODBHDt2jPXr199W\nP5ZMgM8AfsUeNzRvK0Ep9SAwBbhfay1FZaJa+HHvOV6L2k1WbgFKwduDW/NkWCNLh3WNrL3JXIk6\nAkrJvL6i0ikrhX2zutg3q4tbdj5Ze5LJik0i9ccTpP58Avvm7jiG1MOhpYd86BK1hr+/f5UY/R08\neDAnTpwose2dd9655ia6yvDzzz8zadKkEtuaNGnCd999V+G+buWYslgyAd4BNFNKNcGU+D4JlFjO\nRCnVDvg3plKJpLsfohAVczW3gJmr9/Pf7YnYWVthbbBiwbB29A6qb+nQStD5RlJ+OE5m9Dls/Fzw\nGNYCa/eyp9YRojJY2VvjHOaDc5gPeclZZMUmmWaROHgZK0drHNp64RRaHxtfJymREOIuqKxEsjz6\n9OlzRxLr22GxBFhrna+Uehn4GdM0aIu01vuUUjOBGK31KuD/Ac7AcvM/iIla64GWilmIGzlwLo2x\n/93F0aQMHG0NGKwUC59pT1gTd0uHVkKJkocuDXDt6y+jb+KusvFyxLWvP3V6NybnaAqZMefJ3HHe\n9IGsvqNpoY129TA4S4mEEOLOsGgNsNZ6DbCm1LY3i/39wbselBAVpLVmcfRJZq05gIONAUdbA852\n1ix+NowW9avWFGdZe5K5sqKw5CEQh6Bbmz9RiMqgrBT2zeti37wuxqw8ssyzSKT+cILUHxOwD6iL\nU6g39gHu8iFNCFGpqsVNcEJUVZczc/l71G7WHUiilW8djiRl0MDNgS9Gh+Hn7mjp8IroPHPJw9Zz\n2Pq54P5UC6zrSsmDqDqsHG1w7uCDcwcf8i5kkrnTVCKRfeAyVk7WOAbXMy204ets6VCFEDWAJMBC\n3KItRy8yYVkcKVl5DGjjw5q952jd0I1Fz4Ti4Wx38w7ukvyLV7m09AB5ZzNx7toA1z5S8iCqNhtv\nJ9z6NcG1tz/ZR66QFXuBjK3nyPjjLAYPe2zrO2Fd3wkbb0ds6jth7eEg81ULISpEfgsKUUF5BUbe\n/ekgwxduw8nOwJNhfqzec44uzbxYOia8SiW/WbuTuTB/F/lXcvB4OhC3h+6R5FdUG8qgcGjhjsfw\nlvi8Ho7bwKbY+jiRl5RF+vpELi89yIX3Yjnz5h9c+GAnl78+SNrGU1w9eJn8K9lYap57Ie6GhIQE\nli5dWuHjRo4cSVRU1HX3z507l6ysrKLH/fv3JyUl5ZZivFWrVq1i9uzZ190fExPDuHHjANi4cSNb\ntmyp8DlkBFiICki8lMW4r3cRdyqFoaENsTZYsTj6JI8E+/Lu422xrSLJpc4zkrL6GJnbzmPbyFzy\n4CYlD6L6MjjZ4NzJF+dOvoDpPZ6XlEXehUzyLmSRfz6TnBNpZMUlFx2j7Ax/jhJ7O2Lj7YRNfUe5\nuU7UCIUJ8FNPPXXzxhUwd+5cIiIicHQ0lfGtWbPmJkdUvoEDBzJw4PXnPAgNDS1aMW7jxo04OzvT\nqVOnCp1DEmAhymll3BmmfBePUjB3aDBrD1zghz2nebZLE6b0b4mVVdX4CjYvOYvLSw+Sdy4T524N\nce3TGGWoGom5EJVF2Vhh28AZ2wYla4KN2fnkXcgi73wmeeczyb+QxdX4ixi35xe1sXK2MSXG3k5Y\n1zclyDbejljZya/E6i7lf8fIPZtZqX3a+jrh9nDTm7b76quvmDdvHrm5uYSHh/P666/z4IMPEh0d\njbu7O/fffz9Tp06lefPm9O3bl5CQEHbu3ElQUBCLFy/G0dGR2NhYXn31VTIyMvD09CQyMhIfHx+O\nHj3K888/T3JyMgaDgeXLlzN58mQOHDhAcHAwzzzzDOPGjWPy5Mls3LiRnJwcXnrpJZ577jm01owd\nO5a1a9fi5+eHre31PwDOmzePs2fP8sADD+Dp6cmGDRvw9/cnJiaGjIwM+vbtS4cOHdiyZQvt27dn\n1KhRTJs2jaSkJJYsWUJYWBiZmZmMHTuW+Ph48vLymD59OoMGDSrzfB06dGDhwoUEBQUB0L17d+bM\nmUN8fDwxMTEsWLCA5cuXM2PGDAwGA66urmzatImNGzcyZ84cFixYwCeffILBYOCrr75i/vz5dO3a\ntVyvq/y0C3ETGTn5TFu5jxU7TxPSuC5vD27FjNX7+ePoJSb3a8Fz3e6pMvOWZsUlceXboyhrhcfI\nIBxaVK0p2IS406zsrbFrXAe7xn/OwKK1xpiRZ0qKC5PjC1lkxpxH5xqL2hnc7EzJcH1zcuztiE09\nRykbEjd14MABli1bxh9//IGNjQ0vvvgiv/32G5MmTeKFF14gLCyMwMBAevfuTUJCAocOHWLhwoV0\n7tyZ0aNH89FHHzF+/Nv47ucAACAASURBVHjGjh3LypUr8fLyYtmyZUyZMoVFixYxfPhwJk+ezODB\ng8nOzsZoNDJ79mzmzJnD6tWrAfj0009xdXVlx44d5OTk0LlzZ3r37s2uXbs4dOgQ+/fv5/+zd+Zh\nclVl/v+cu9RevaSz0elsIEkgO1kAWWQZSFQwgJE1AiKL44ygg4yOGgVFR4XHYWQEXACFIWxRILIo\n89MERCAhHQJElqydpLP33rXfe8/5/XFvVVf1ls7SWe8nz3nOfu6p6krV9773Pefs2LGDE088keuu\nu67b13HzzTfzs5/9jMWLFzNwYNeDkdauXcvTTz/NQw89xIwZM1iwYAGvvfYaixYt4kc/+hHPPvss\nP/zhDznnnHN46KGHaGlpYebMmfzTP/0T0Wi0y3iXXXYZTz31FHfccQfbtm1j27ZtTJ8+veSgkO9/\n//v8+c9/ZtiwYV1cMUaNGsWXvvQlYrEYX//61/fob+YLYB+fXni3voWbH3+bTU0pbj73eK6aOZwv\nPrKcD7a1c/fnJjN3Ws3BniIAynJo+eN6ksu2ExhZxoArxmFUHDq+yD4+BxMhBHo8gB4PEDq+slCu\npMJpyXqCOIm1PYW9I0lmTTM4nv+w5h7tbA4pWnQ3NIoxIIQ4RJ76+HTQF0ttf/CXv/yF2tpaZsyY\nAUA6nWbw4MHcfvvtPP300zzwwAOsXLmy0H748OGcdtppAMybN4+f//znzJ49m1WrVnHeeecB4DgO\nxxxzDO3t7WzZsoWLL74YgFCoe3e2l19+mXfffbfg39va2sqaNWt49dVXueKKK9B1nerqas4555y9\nfp2jR49m4sSJAIwfP55zzz0XIQQTJ06krq6uMI9FixZx9913A5DJZNi0aRMnnHBCl/EuvfRSzj//\nfO644w6eeuop5s6d26XNaaedxrXXXsull17KJZdcstdz74wvgH18ukFKxW9eW89df/6IgbEgj99w\nCseUh7nsV2+yvS3Dr6+exjnjhhzsaQKey8NjH2JtTxL7RA3l5/suDz4+fUFoAmNACGNAiPCJHXti\nK0diN6SxtqcKwji3NUF6VQPk19UZmudG0eFCYQyNopcFDpknQj4HDqUU11xzDf/5n/9ZUp5Kpaiv\nrwcgkUgQj8cBunxGhBAopRg/fjxvvPFGSV17e3uf53Dvvfd2OXFtf/rwBoMdhhVN0wp5TdOwbbsw\nj9///veMHTt2t+MNGzaMqqoq3n33XZ588kkeeOCBLm0eeOABli5dygsvvMC0adOora3dL6/FF8A+\nPp3Y2Z7h1qfe4W9rGpg1fgg/+ewktrSkueT+17EcyWPXn8K0kZW7H+gA4Ls8+Pjsf4SueRbfKDCo\nUC5zDvbOlCuMPatxZm0LqRU7O/qGDMyhEYyKICJsoIUMNC8WYb1T3kAL6f4N6xHAueeey5w5c/ja\n177G4MGDaWpqor29nbvvvpurrrqKkSNHcsMNNxTcFTZt2sQbb7zBqaeeyoIFCzj99NMZO3Ysu3bt\nKpRblsXq1asZP348NTU1PPvss1x00UVks1kcxyEej5eI41mzZnH//fdzzjnnYJomq1evZtiwYZx5\n5pn88pe/5JprrmHnzp0sXry414Vz+XG7c4HoC7NmzeLee+/l3nvvRQjB22+/zdSpU3tsf9lll/HT\nn/6U1tZWJk2a1KV+3bp1nHzyyZx88sm89NJLbN68uct829ra9nievgD28Sli8Uc7ue3pd2jP2Pzw\n4glcOXMEb6xv5MZHaomHDB6/4VSOHxI/2NN0XR4WrSf5lufycOU4jHLf5cHHpz/RAjqBmjiBmtLv\nAJmyOqzFno9xdnM7Km0jMzbIHgb0EKbWSSzrfRbPWsjwfZQPAU488UTuvPNOzj//fKSUmKbJz372\nM9566y3+/ve/o+s6v//973n44Yc5++yzGTt2LL/4xS+47rrrOPHEE/nnf/5nAoEACxcu5Oabb6a1\ntRXbtvnqV7/K+PHjefTRR7npppv47ne/i2maPP3000yaNAld15k8eTLXXnstt9xyC3V1dZx00kko\npRg0aBDPPvssF198MX/961858cQTGTFiBKeeemqvr+XGG29k9uzZVFdXs3jx4j1+L+bPn89Xv/pV\nJk2ahJSS0aNHF4R/d8ydO5dbbrmF+fPnd1t/2223sWbNGpRSnHvuuUyePJlXXnmlUH/hhRcyd+5c\nnnvuuT1aBCeOtH0Sp0+frpYvX36wp+FzmJG1HX76p4948LUNjBsa5+dXTGXMkDgvvreNrz6xkpFV\nEX533UyqK8IHe6pYO1M0LfgAa3uK+FnDKTtvpH8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DWVkZDQ0NnHLKKXzmM5/hT3/6E9XV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\nTPyQwMAYX4fULoqLK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ojIMhEJtepcICKzrOVLrVbZLBF5Shq34g+3Xu8dInKnW0zfEZFv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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "for f in feats:\n",
    "    plt.plot(Rpath1.index.values, Rpath2[[f]], label=f)\n",
    "\n",
    "plt.xlim([-4, 2])\n",
    "plt.ylim([-0.5, 0.5])\n",
    "box = ax.get_position()\n",
    "ax.set_position([box.x0, box.y0, box.width*1.5, box.height * 1.5])\n",
    "\n",
    "    # Put a legend below current axis\n",
    "ax.legend(loc='upper center', bbox_to_anchor=(1.15, 1), fancybox=True, shadow=True, ncol=1, prop={'size':10})\n",
    "\n",
    "plt.title('L1 Regularization Paths for Feature Weights.')\n",
    "plt.xlabel('Regularization weight C (higher C is less regularization)')\n",
    "plt.ylabel('Feature Weight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>It is not so obvious from the above plot that $L1$ holds the feature weight at 0 for some time, but we can see this if we directly compare the paths of individual features.\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4481U6GQfrrgSZOJEu9GrVbOwMAcckPi5jRvb053jOEVZscJGWosXw0cfhf+A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\nkhUNXCIikpUv04bXcl5enw4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fs = ['isbuyer','expected_time_visit','visit_freq','multiple_buy']\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "for i,f in enumerate(fs):\n",
    "    fig.add_subplot(2, 2, i+1)\n",
    "    plt.title(f)\n",
    "    plt.plot(Rpath2.index.values, Rpath2[[f]], 'b', label='L2')\n",
    "    plt.plot(Rpath1.index.values, Rpath1[[f]], 'b--', label='L1')\n",
    "    \n",
    "fig.tight_layout()\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Next we want to choose our regularization strength. Remember that from a Bayesian point of view, the regularization strength respresents our prior belief on the variance of the feature weights. If we assume a lower prior variance, we are effectively not allowing the weights to deviate too far from zero. Whether we take this point of view or not, the optimal strength is largely an empirical question. It is generally better to test rather than to assume what the optimal strength should be. <br><br>\n",
    "\n",
    "The various implementations of learning algorithms differ in how they treat the regularization parameter. Many implementations formulate the loss function as such:<br><br>\n",
    "\n",
    "<center>$\\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda R(W)$\n",
    "</center><br><br>\n",
    "In the above, the parameter $\\lambda$ controls how much of the loss function is determined by the regularization function. Other implementations view it like this:<br><br>\n",
    "<center>\n",
    "$\\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n C*\\mathbb{L}(f(x_i),y_i)+R(W)$\n",
    "</center><br><br>\n",
    "In the latter formulation the parameter controls how much the training error influences the total loss. It doesn't really matter which of the above is used (one is just a scalar multuple of the other), but it is helpful to know which system your implementation uses. I.e., it is useful to know if increasing the regularization parameter <i>increases</i> or <i>decreases</i> the amount of regularization being done. In SKLearn, the latter formulation is used.<br><br>\n",
    "\n",
    "Here we take the above example and use cross validation to find an optimal regularization strength.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "from sklearn.metrics import roc_auc_score\n",
    "\n",
    "def LRValAUC(X_tr, Y_tr, k, cs):\n",
    "    '''\n",
    "    Perform k-fold cross validation on logistic regression, varies C and penalty Type (L1 or L2),\n",
    "    returns a dictionary where key=c,value=[auc-c1, auc-c2, ...auc-ck].\n",
    "    '''\n",
    "    cv = KFold(n_splits=10)\n",
    "    aucs = {}\n",
    "\n",
    "    for train_index, test_index in cv.split(X_tr):\n",
    "        X_tr_f = X_tr.iloc[train_index]\n",
    "        X_va_f = X_tr.iloc[test_index]\n",
    "        Y_tr_f = Y_tr.iloc[train_index]\n",
    "        Y_va_f = Y_tr.iloc[test_index]\n",
    "        \n",
    "        for c in cs:\n",
    "            for norm in [1,2]:\n",
    "                lr = linear_model.LogisticRegression(C=c, penalty='l{}'.format(norm))\n",
    "                lr.fit(X_tr_f,Y_tr_f)\n",
    "                met = roc_auc_score(Y_va_f, lr.predict_proba(X_va_f)[:,1])\n",
    "\n",
    "                if (c, norm) in aucs:\n",
    "                    aucs[(c, norm)].append(met)\n",
    "                else:\n",
    "                    aucs[(c, norm)] = [met]\n",
    "    \n",
    "    return aucs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xval_dict = {'e':[], 'mu':[], 'sig':[], 'norm':[]}\n",
    "k = 10\n",
    "exps = np.arange(-5,5,0.5)\n",
    "auc_cv = LRValAUC(X_train, Y_train, k, [10**i for i in exps])\n",
    "for i in exps:\n",
    "    for norm in [1, 2]:\n",
    "        xval_dict['e'].append(i)\n",
    "        xval_dict['norm'].append(norm)\n",
    "        xval_dict['mu'].append(np.array(auc_cv[(10**i, norm)]).mean())\n",
    "        xval_dict['sig'].append(np.sqrt(np.array(auc_cv[(10**i, norm)]).var()))\n",
    "\n",
    "xvals = pd.DataFrame(xval_dict)\n",
    "xvals['low'] = xvals['mu']-xvals['sig']/np.sqrt(k)\n",
    "xvals['up'] = xvals['mu']+xvals['sig']/np.sqrt(k)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now lets plot the cross-validated error as a function of C, with a separate series for the different penalization types\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wZFNJX6RV+vTp02DfSy+9xJFHHklubi6PPfZYu8ShpC/7pikYRNrMiBEjuP/+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\nW0gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "\n",
    "norm = 1\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'r')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'r--', label='L1')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'r+')\n",
    "\n",
    "norm = 2\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'b')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'b--', label='L2')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'b+')\n",
    "\n",
    "plt.legend(loc=4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This is interesting. We can see that the AUC for $L1$ is $0.5$ where the regularization is stronger, but for $L2$ the AUC is pretty good in the same region. This is because all of the feature weights in $L1$ are zero for that range. In $L2$ they'll likely be small, but they won't be zero. This means they'll still be able to rank the instances.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Nc6FIyI4d9oBOO80mmnAcJ3IqbOAOo6rTgeki8mvg6MyZVP/45BP4xS9s1PWF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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm = 1\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'r')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'r--', label='L1')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'r+')\n",
    "\n",
    "norm = 2\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'b')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'b--', label='L2')\n",
    "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'b+')\n",
    "\n",
    "plt.legend(loc=4)\n",
    "plt.ylim([0.82, 0.89])\n",
    "\n",
    "plt.title('X-Val AUC by Regularization Weight')\n",
    "plt.xlabel('Regularization weight C (higher C is less regularization)')\n",
    "plt.ylabel('X-Val AUC')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
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